Four Tenth Roots

★ 6/10complex numbers Roots of Unity Filter algebra Polynomials

Problem

Let $\omega = \cos\dfrac{\pi}{5} + \mathrm{i}\sin\dfrac{\pi}{5}$ . Expand

(x - \omega)(x - \omega^3)(x - \omega^7)(x - \omega^9)

as a polynomial in $x$ with integer coefficients.

Answer

Solution

Difficulty	6/10
Topics	complex numbers, Roots of Unity Filter, algebra, Polynomials

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